Fix WooCommerce product sync button functionality

- Move sync handler from wc-integration.js to admin.js (uses wpBnbAdmin)
- Add CSS for button icon vertical alignment with inline-flex
- Add spin animation for sync button icon during operation
- Add sync status styling (success/error colors)
- Add i18n strings for syncing messages

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

assets/css/admin.css

@@ -2098,3 +2098,45 @@
 	width: 16px;
 	height: 16px;
 }
+
+/* ============================================
+   WooCommerce Sync Button
+   ============================================ */
+.bnb-sync-rooms-btn {
+	display: inline-flex;
+	align-items: center;
+	gap: 6px;
+}
+
+.bnb-sync-rooms-btn .dashicons {
+	font-size: 16px;
+	width: 16px;
+	height: 16px;
+	line-height: 1;
+}
+
+.bnb-sync-rooms-btn .dashicons.bnb-spin {
+	animation: bnb-spin 1s linear infinite;
+}
+
+@keyframes bnb-spin {
+	from {
+		transform: rotate(0deg);
+	}
+	to {
+		transform: rotate(360deg);
+	}
+}
+
+.sync-status {
+	margin-left: 10px;
+	font-style: italic;
+}
+
+.sync-status .bnb-sync-success {
+	color: #00a32a;
+}
+
+.sync-status .bnb-sync-error {
+	color: #d63638;
+}